KABUL—Mawlawi Zubair Mutmaeen used to run Taliban suicide-bombing squads in Kabul. On a recent day, in his new role as police chief for one of the Afghan capital’s districts, he was busy mediating a marital dispute.

A woman clad in a burqa complained she could no longer live with her interfering mother-in-law. Clearly used to being in command, Mr. Mutmaeen lectured the husband that under Islamic law he must provide his wife with “shelter and other basic necessities.”

Mr....

KABUL—Mawlawi Zubair Mutmaeen used to run Taliban suicide-bombing squads in Kabul. On a recent day, in his new role as police chief for one of the Afghan capital’s districts, he was busy mediating a marital dispute.

A woman clad in a burqa complained she could no longer live with her interfering mother-in-law. Clearly used to being in command, Mr. Mutmaeen lectured the husband that under Islamic law he must provide his wife with “shelter and other basic necessities.”

Mr. Mutmaeen’s solution was to have the mother relocate to the home of her other son. After some persuading, the husband reluctantly agreed.

His face framed by a black turban and black beard, Mr. Mutmaeen didn’t see the jarring change from his previous occupation as remarkable. In the past, Americans and locals who worked with them were legitimate targets as the Taliban sought to create a true Islamic order, he said.  Today, he reasoned, community policing serves the same goal.

“Previously I was serving Islam, and now I’m also serving Islam. There is no difference,” Mr. Mutmaeens, 39, said.

The Taliban-turned-cops under Mr. Mutmaeen’s command aren’t being paid, and they haven’t received training in actual police work. It isn’t clear what laws they are enforcing, other than their understanding of the Islamic Shariah. The penal code of the U.S.-backed Afghan republic, deposed by the Taliban on Aug. 15, may or may not be in force. The Taliban have said they aim to bring back the 1964 constitution from the era of King Zahir Shah—minus unspecified clauses they see as contradicting Islam.

Mawlawi Zubair Mutmaeen, a Taliban police chief, talks to people who came to his office for help.

The same haphazard approach permeates the rest of Afghanistan’s government bureaucracy, where thousands of educated professionals abandoned their jobs or left the country in August. The Taliban appointed Islamic clerics with little management experience to run ministries and government departments. As of this month, the country’s electric utility company, which hasn’t paid its foreign power suppliers or collected much revenue at home since Aug. 15, is headed by a mullah.

With Afghanistan’s harsh winter approaching and economic activity paralyzed after the banking system seized up in August, challenges are mounting.

“There is no indication that the Taliban has any idea how to run a country,” said Asfandyar Mir, a senior expert at the United States Institute of Peace, a bipartisan federal institution established by Congress and based in Washington.

Even the Taliban’s main strength—providing security—is being tested by a ferocious campaign of attacks by the regional affiliate of the Islamic State militant group, including two bombings this month at mosques used by the minority Shiite Muslims, which killed dozens.

At Kabul’s new primary court, housed in the former ministry of public works, no trials are taking place, according to court staff. Instead, the court is hosting mediation to resolve disputes. If the parties can’t reach a compromise, a case file is prepared for a future hearing before a judge.

The Taliban ran shadow courts in areas they controlled before seizing power. A 2020 study by the Overseas Development Institute, a think tank in London that does research on global inequality, found many locals believed these Taliban courts delivered swifter, fairer and less-corrupt justice than the U.S.-backed government system.

Shariah law, which derives from the Quran and the sayings and deeds of the Prophet Muhammad, covers both criminal and civil cases, as well as moral conduct. It has harsh penalties for some misdemeanors, including whipping for adultery and cutting off a hand for theft. The Taliban gained notoriety for applying these punishments when they were last in power, between 1996 and 2001. Most Muslim-majority countries today don’t carry them out.

Taliban police stand guard outside a mosque during Friday prayers.

Taking an ice-cream break.

A guerrilla group numbering tens of thousands of fighters, the Taliban governed only remote rural areas until this year. Foot soldiers were not formally paid and war booty provided irregular earnings. Fighters say they were supported by other family members who had paid employment.

Now the war is over, the Taliban have to find a way to add these men to the government payroll at a time when Afghan government coffers are empty, most foreign aid is suspended and some $9 billion in Afghan central-bank assets are frozen in the U.S.

The ousted administration of President Ashraf Ghani stopped paying salaries to government employees nearly two months before the Taliban takeover. The Taliban have since managed to pull together enough funds to provide one month’s salary to most of the existing employees at ministries in Kabul, said officials in the education and finance ministries.

The finance ministry is now raising more than $2 million a day in revenues, mostly from customs duties, said Ahmad Wali Haqmal, a spokesman for the ministry and a member of the Taliban who says he holds a master’s degree in human rights from Aligarh Muslim University in India.

“We will stop the corruption that was previously taking money out of the system, and we will have no war expenses. That way, we will be able to cover our costs,” he said.

The Taliban have been trying to project an image of safety and normalcy since retaking power. But as WSJ’s Sune Rasmussen reports from Kabul, harsh punishments, violence, and a crackdown on basic freedoms are becoming the reality. Photo: Bulent Kilic/AFP/Getty Images The Wall Street Journal Interactive Edition

Most male workers at government ministries have drifted back. Female employees have been told by the Taliban to stay home, at least for now.

The Taliban’s new police force in Kabul represents the most visible change, with only a few of the old cops returning to service—and even then only for back-office duty, without their guns. On Aug. 15, as Mr. Ghani surprised Afghans by fleeing the country, police officers working for his government took off their uniforms and abandoned their duties. The Taliban cited the unraveling of public order as the reason they entered Kabul, violating their promises of seeking a negotiated settlement.

These days, heavily armed, battle-hardened Taliban fighters patrol the city of six million, many in old police uniforms but with shoulder-length hair and bushy beards that indicate their true identities. They cruise around in U.S.-supplied Ford Rangers, brandishing American M-16 assault rifles, and operate out of sprawling police stations built by American taxpayers.

Former Taliban fighters now patrol the streets of Kabul, a city of six million.

Mr. Mutmaeen, who runs the 9th police district in Kabul, used to gather intelligence, find weak spots in targets and order in suicide bombings for the Haqqani Network, the faction of the Taliban designated by the U.S. as a global terrorist organization because of its close links to al Qaeda. Mr. Mutmaeen said he joined the insurgency at 17 in his home province of Logar, south of the capital. Living under cover in Kabul, he operated a web of informers inside the previous government.

The Haqqani Network hit Kabul relentlessly, pulling off many of the most lethal attacks in the capital. Among the assaults Mr. Mutmaeen said he ordered were on the presidential palace, a CIA office and the Kabul Serena hotel, which was struck multiple times over the years and where much of the foreign media is currently staying, under Taliban protection.

The bickering couple were among a long line of residents of Kabul’s 9th district who had come to see their new police chief. Mr. Mutmaeen called them over one by one, asking them to sit at the side of his desk. They talked in low voices, heads almost touching. Then he made a phone call or instructed one of his underlings to find a solution.

At first, Kabul residents were nervous about approaching the Taliban’s new police. Now the office is crowded.  Some want Taliban help to get debtors to pay up. Others complain about stolen cars. Some are looking for a job.

Invisible, of course, are the many people of Kabul who are hiding in their homes in dread of the Taliban. Many who missed the U.S.-led airlift in August, which flew out more than 120,000 people, are still desperately seeking to escape abroad. Fewer women are seen walking on the streets and only a fraction of them have been able to return to work.

Those disapproving of the Taliban hesitate to raise their voices, including anyone critical of the group’s police. The Taliban have cracked down on small-scale demonstrations that have taken place in Kabul and other cities, firing in the air and hitting women who demanded equal rights. Two journalists working for Afghan newspaper Etilaatroz, covering a women’s protest in Kabul last month, were taken away by the Taliban and severely beaten in a police station. They were hit with cables and batons, Etilaatroz reported, and needed hospital treatment when they were released later that day. A Taliban official later visited the newspaper and promised an investigation.

Mawlawi Zubair Mutmaeen takes a call in his office.

The scene outside the 9th district precinct police station.

The police service of the deposed Afghan republic was notoriously corrupt, according to reports of the Special Inspector General for Afghanistan Reconstruction, a watchdog created by Congress, and was also accused of widespread human-rights abuses. Mr. Mutmaeen said he’s keeping the few members of the old police who have returned out of sight in the back of his station. “The people really hated the old police. If they see them here, with me, they will think that nothing has changed,” he said.

In Kabul’s 12th police district, Mohammad Ibrahim had been trying to collect an $8,500 debt for three years. He had supplied fuel to an influential local businessman, who he said refused to pay. He said he didn’t approach the previous police given his opponent’s connections with politicians in the fallen republic.

Last month, Mr. Ibrahim went to the new Taliban cops, who arrested the debtor, he said. Now the Taliban plan to bring both parties together for arbitration. “I was sure the old police would not care about my problem,” said Mr. Ibrahim, who said he didn’t have a prior relationship with the Taliban.

A senior police officer in the 12th district, Qari Fasi, said the Taliban weren’t seeking retribution against members of the fallen regime and its security forces. “We forgive everyone,” he said. “Our duty is to protect everyone now.”

Many residents say crime has gone down since the Taliban takeover. Kabul residents said they have been able to travel by road to parts of the country that were far too dangerous before.

Taliban fighter-turned-policeman Hajji Naseem, who comes from a rural area of Ghazni province, headed a vehicle patrol on a recent day in an SUV with pickup trucks of his men following. A subordinate, in the front passenger seat, used Google Maps to navigate the unfamiliar streets of Kabul.

Mawlawi Hamza, police chief of the 8th district, poses with his men.

Coasting slowly in their new uniforms, bristling with guns, the men stopped at a few places and jumped out. Some locals approached them gingerly to chat, already seemingly adjusted to their presence, while little kids ran forward, fascinated.

Ehsanullah Hussainkhil, a youth organizer in Kabul, hosted a lunch of kebabs and rice for the Taliban police officers in a local restaurant. Initially, he said, he was scared of them.

“There was a barrier. Because of their image, we were terrified they will kill us,” he said, as the Taliban seated at the table looked on and listened. “But as we are gradually getting acquainted with them, we see that they are good.”

Police work, it turned out, is more stressful than jihad—and big-city problems aren’t what Mr. Naseem’s men were used to in the rural backwaters.

“Jihad was a glorious time. The fighting was hard, we ate little, but we could become heroes,” said Mr. Naseem, the administrative head of Kabul’s 8th police district. “Now I can’t sleep through the night because I am worrying that maybe a robbery is happening some place, or a woman is being beaten by a family member.”

Write to Saeed Shah at saeed.shah@wsj.com